Heatmap

Evaluate the effect of centering & scaling

1-correlation distance

Effect of centering and scaling on clustering of genes and samples in terms of distance. 'Yes' means the distance was changed compared to the baseline where no centering or scaling was applied.

	clustering genes	clustering samples
centering on each genes	No	Yes
scaling on each genes	No	Yes

Euclidean distance

	clustering genes	clustering samples
centering on each genes	Yes	No
scaling on each genes	Yes	Yes

Supporting R code

1. 1-Corr distance

source("http://www.bioconductor.org/biocLite.R")
biocLite("limma"); biocLite("ALL")

library(limma); library(ALL)
data(ALL)

eset <- ALL[, ALL$mol.biol %in% c("BCR/ABL", "ALL1/AF4")]

f <- factor(as.character(eset$mol.biol))
design <- model.matrix(~f)
fit <- eBayes(lmFit(eset,design))
selected  <- p.adjust(fit$p.value[, 2]) < 0.05
esetSel <- eset [selected, ]   # 165 x 47
heatmap(exprs(esetSel))

esetSel2 <- esetSel[sample(1:nrow(esetSel), 20), sample(1:ncol(esetSel), 10)] # 20 x 10

dist.no <- 1-cor(t(as.matrix(esetSel2))) 
dist.mean <- 1-cor(t(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2))))) # gene variance has not changed!
dist.median <- 1-cor(t(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median))))

range(dist.no - dist.mean) # [1] -1.110223e-16  0.000000e+00
range(dist.no - dist.median) # [1] -1.110223e-16  0.000000e+00
range(dist.mean - dist.median) # [1] 0 0

So centering (no matter which measure: mean, median, ...) genes won't affect 1-corr distance of genes.

dist.mean <- 1-cor(t(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)), "/")))
dist.median <- 1-cor(t(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median), "/")))
range(dist.no - dist.mean) # [1] -8.881784e-16  6.661338e-16
range(dist.no - dist.median) # [1] -6.661338e-16  6.661338e-16
range(dist.mean - dist.median) # [1] -1.110223e-15  1.554312e-15

So scaling after centering (no matter what measures: mean, median,...) won't affect 1-corr distance of genes.

How about centering / scaling genes on array clustering?

dist.no <- 1-cor(as.matrix(esetSel2))
dist.mean <- 1-cor(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)))) # array variance has changed!
dist.median <- 1-cor(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median)))

range(dist.no - dist.mean) # [1] -1.547086  0.000000
range(dist.no - dist.median) # [1] -1.483427  0.000000
range(dist.mean - dist.median) # [1] -0.5283601  0.6164602

dist.mean <- 1-cor(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)), "/"))
dist.median <- 1-cor(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median), "/"))
range(dist.no - dist.mean) # [1] -1.477407  0.000000
range(dist.no - dist.median) # [1] -1.349419  0.000000
range(dist.mean - dist.median) # [1] -0.5419534  0.6269875

2. Euclidean distance

dist.no <- dist(as.matrix(esetSel2))
dist.mean <- dist(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2))))
dist.median <- dist(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median)))

range(dist.no - dist.mean) # [1] 7.198864e-05 2.193487e+01
range(dist.no - dist.median) # [1] -0.3715231 21.9320846
range(dist.mean - dist.median) # [1] -0.923717629 -0.000088385

Centering does affect the Euclidean distance.

dist.mean <- dist(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)), "/"))
dist.median <- dist(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median), "/"))

range(dist.no - dist.mean) # [1]  0.7005071 24.0698991
range(dist.no - dist.median) # [1]  0.636749 24.068920
range(dist.mean - dist.median) # [1] -0.22122869  0.02906131

And scaling affects Euclidean distance too.

How about centering / scaling genes on array clustering?

dist.no <- dist(t(as.matrix(esetSel2)))
dist.mean <- dist(t(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)))))
dist.median <- dist(t(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median))))

range(dist.no - dist.mean) # 0 0
range(dist.no - dist.median)  # 0 0
range(dist.mean - dist.median) # 0 0

dist.mean <- dist(t(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)), "/")))
dist.median <- dist(t(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median), "/")))

range(dist.no - dist.mean) # [1] 1.698960 9.383789
range(dist.no - dist.median)  # [1] 1.683028 9.311603
range(dist.mean - dist.median) # [1] -0.09139173  0.02546394

Simple image plot using image() function

https://chitchatr.wordpress.com/2010/07/01/matrix-plots-in-r-a-neat-way-to-display-three-variables/

### Create Matrix plot using colors to fill grid
# Create matrix.   Using random values for this example.
rand <- rnorm(286, 0.8, 0.3)
mat <- matrix(sort(rand), nr=26)
dim(mat)  # Check dimensions
 
# Create x and y labels
yLabels <- seq(1, 26, 1)
xLabels <- c("a", "b", "c", "d", "e", "f", "g", "h", "i",
"j", "k");
 
# Set min and max values of rand
 min <- min(rand, na.rm=T)
 max <- max(rand, na.rm=T)
 
# Red and green range from 0 to 1 while Blue ranges from 1 to 0
 ColorRamp <- rgb(seq(0.95,0.99,length=50),  # Red
                  seq(0.95,0.05,length=50),  # Green
                  seq(0.95,0.05,length=50))  # Blue
 ColorLevels <- seq(min, max, length=length(ColorRamp))
 
# Set layout.  We are going to include a colorbar next to plot.
layout(matrix(data=c(1,2), nrow=1, ncol=2), widths=c(4,1),
         heights=c(1,1))
#plotting margins.  These seem to work well for me.
par(mar = c(5,5,2.5,1), font = 2)
 
# Plot it up!
image(1:ncol(mat), 1:nrow(mat), t(mat),
     col=ColorRamp, xlab="Variable", ylab="Time",
     axes=FALSE, zlim=c(min,max),
     main= NA)
 
# Now annotate the plot
box()
axis(side = 1, at=seq(1,length(xLabels),1), labels=xLabels,
      cex.axis=1.0)
axis(side = 2, at=seq(1,length(yLabels),1), labels=yLabels, las= 1,
      cex.axis=1)
 
# Add colorbar to second plot region
par(mar = c(3,2.5,2.5,2))
 image(1, ColorLevels,
      matrix(data=ColorLevels, ncol=length(ColorLevels),nrow=1),
      col=ColorRamp,xlab="",ylab="",xaxt="n", las = 1)

If we define ColorRamp variable using the following way, we will get the 2nd plot.

require(RColorBrewer) # get brewer.pal()
ColorRamp <- colorRampPalette( rev(brewer.pal(9, "RdBu")) )(25)

Note that

• colorRampPalette() is an R's built-in function. It interpolate a set of given colors to create new color palettes. The return is a function that takes an integer argument (the required number of colors) and returns a character vector of colors (see rgb()) interpolating the given sequence (similar to heat.colors() or terrain.colors()).
• brewer.pal(9, "RdBu") creates a diverging palette based on "RdBu" with 9 colors. See help(brewer.pal, package="RColorBrewer") for a list of palette name. The meaning of the palette name can be found on colorbrew2.org website.

gplots package

The following example is extracted from DESeq2 package.

## ----loadDESeq2, echo=FALSE----------------------------------------------
# in order to print version number below
library("DESeq2")

## ----loadExonsByGene, echo=FALSE-----------------------------------------
library("parathyroidSE")
library("GenomicFeatures")
data(exonsByGene)

## ----locateFiles, echo=FALSE---------------------------------------------
bamDir <- system.file("extdata",package="parathyroidSE",mustWork=TRUE)
fls <- list.files(bamDir, pattern="bam$",full=TRUE)


## ----bamfilepaired-------------------------------------------------------
library( "Rsamtools" )
bamLst <- BamFileList( fls, yieldSize=100000 )


## ----sumOver-------------------------------------------------------------
library( "GenomicAlignments" )
se <- summarizeOverlaps( exonsByGene, bamLst,
                         mode="Union",
                         singleEnd=FALSE,
                         ignore.strand=TRUE,
                         fragments=TRUE )

## ----libraries-----------------------------------------------------------
library( "DESeq2" )
library( "parathyroidSE" )

## ----loadEcs-------------------------------------------------------------
data( "parathyroidGenesSE" )
se <- parathyroidGenesSE
colnames(se) <- se$run

## ----fromSE--------------------------------------------------------------
ddsFull <- DESeqDataSet( se, design = ~ patient + treatment )

## ----collapse------------------------------------------------------------
ddsCollapsed <- collapseReplicates( ddsFull,
                                    groupby = ddsFull$sample, 
                                    run = ddsFull$run )

## ----subsetCols----------------------------------------------------------
dds <- ddsCollapsed[ , ddsCollapsed$time == "48h" ]

## ----subsetRows, echo=FALSE----------------------------------------------
idx <- which(rowSums(counts(dds)) > 0)[1:4000]
dds <- dds[idx,]

## ----runDESeq, cache=TRUE------------------------------------------------
dds <- DESeq(dds)

rld <- rlog( dds)

library( "genefilter" )
topVarGenes <- head( order( rowVars( assay(rld) ), decreasing=TRUE ), 35 )

## ----beginner_geneHeatmap, fig.width=9, fig.height=9---------------------
library(RColorBrewer)
library(gplots)
heatmap.2( assay(rld)[ topVarGenes, ], scale="row", 
           trace="none", dendrogram="column", 
           col = colorRampPalette( rev(brewer.pal(9, "RdBu")) )(255))